The GDP deflator in Japan

We have already mentioned that Japan is the best illustration of our concept linking inflation/unemployment to the change in labour force. In the previouspost on inflation in Japan, we modelled the overall CPI. Here we illustrate the long term equilibrium relation between the GDP deflator, DGDP, and labour force. All data were obtained from the OECD.

By trial-and-error, we seek for the best-fit coefficients in the linear and lagged link between inflation and labour force. Because of the structural (measurement related?) break in the 1980s, we have chosen the period after 1981 for linear regression, which is common for almost all economic studies related to Japan. By varying the lag and coefficients we have found the following relationship:

DGDP(t)= 1.9dLF(t-t₀)/LF(t-t₀) – 0.0084        (1)

where the time lag t₀=0 years; Figure 1 depicts this best-fit case. There is no time lag between the inflation series and the labour force change series in Japan. Free term in (1), defining the level of price inflation in the absence of labour force change, is close to zero but negative.

A more precise and reliable representation of the observed and predicted inflation consists in the comparison of cumulative curves shown in the lower panel of Figure 1. We always stress that the cumulative values of price inflation and the change in labour force are the levels of price and labour force, respectively. Therefore, the summation of the annual reading gives the original estimates of price and workforce, which when are converted into rates.

Another advantage of the cumulative curves is that all short-term oscillations and uncorrelated noise in data as induced by inaccurate measurements and the inevitable bias in all definitions are effectively smoothed out. Any actual deviation between these two cumulative curves persists in time if measured values are not matched by the defining relationship. The predicted cumulative values are very sensitive to free term in (1).

For Japan, the DGDP cumulative curves are characterized by very complex and unusual for economics shapes. There was a period of intensive inflation growth and a long deflationary period. The labour force change, defining the predicted inflation curve, follows all the turns in the measured cumulative inflation with the coefficient of determination R²=0.96. (Again, these are actually measured curves.) With shrinking population, and thus, labour force, the GDP deflator will be falling through 2050 and likely beyond.

Figure 1. Measured GDP deflator and that predicted from the change rate of labour force. Upper panel:  Annual curves smoothed with MA(3). Lower panel: Cumulative curves between 1981 and 2010. A good agreement between the cumulative curves illustrates the predictive power of our model.

The anti-Phillips curve indicates that the rate of unemployment in the UK must drop below 7% by the end of 2013.

We introduced a model of unemployment in the USA and other developed countries six years ago. The rate of unemployment, u_t, and price inflation, CPI_t, are driven by the same force - the rate of change of labour force. Briefly, there exists a long-term equilibrium (linear and lagged) link between unemployment, inflation and labour force. As a consequence, the rate of inflation and unemployment are also linked by a linear and lagged relationship.  In the USA, unemployment lags behind both CPI and labour force by 3 and 5.5 years, respectively. This creates a situation contradicting any mainstream macroeconomic theory. Under the conventional framework, which is usually described by the Phillips curve, the change in unemployment must be contemporary or leading price inflation. As a joke, we proposed to call the actual link between inflation and unemployment in the USA the anti-Phillips curve. As always, the economics profession ignores observations and looks for the answer in the reservation limited by theoretical barbed wire.  Here we present the case of the United Kingdom. Monthly estimates of the rate of unemployment and CPI, both obtained from the OSCD, completely confirm the concept of the anti-Phillips curve. Unemployment in the UK lags behind inflation by 24 months.

In practice, we are looking for the best-fit linear and lagged equation in the following form:

u_t = aCPI_t-j  + b      (1) 

where a and b are empirical coefficients, and j is the time lag between these variables, which can be positive, zero, or negative. Figure 1 displays the best fit model with a=0.9, b=0.041 and j=24 months. Since the monthly estimates of CPI_t are very noisy we have smoothed the predicted curve with MA(24). Overall, the rate of unemployment repeats the shape of the scaled inflation curve two years later.  The coefficient of determination R²=0.89 for the period between 1981 and 2011, i.e. for 360 readings.

From Figure 1 one can conclude that there exists an anti-Phillips curve in the UK as it was revealed for the USA. Inflation does lead unemployment and the economic theory can not ignore this observation. A good validation of the model would be the fall in the rate of unemployment in the UK below 7% by the end of 2013. The observed curve should intercept the predicted one in the near future.

Figure 1. Observed and predicted rate of unemployment in the UK. Lower panel presents the cumulative values of the curves in the upper panel. This is the best control of the link.

Labour force participation in Sweden and the Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel

We have published a number of models for the rate of participation in labour force, LFP. The intuition behind the model is very simple. The growth in real GDP influences the labour force supply through redistribution of personal incomes. Fluctuations in real GDP per capita relative to that defined by inertial economic growth, A₁/G, provide variations in the distribution of personal income relative to some inertial (or neutral) growth rate. The influence of the growth in real GDP on the LFP has to be complicated by the presence of exponential distribution of personal inputs to real GDP. If the effect of real growth is based on the excess of the total personal income above its potential (inertia) level, then higher levels of LFP are more sensitive to real growth. Really, more people can be included in or excluded from the redistribution because of their smaller personal incomes for paid jobs, which are replaced by some other (not measured) mechanisms of personal income earning. It is reasonable to assume that the sensitivity of LFP to the difference between actual and potential (inertial) growth rates, e(t)=dG/G–A/G, grows exponentially with increasing LFP. In addition, there might be a time delay between action and reaction and the LFP may lag behind the e(t). Now we are ready for a quantitative analysis with a tentative relationship: 

{B₁dLFP(t)/LFP(t) + C₁}exp{ a₁[LFP(t) - LFP(t₀)]/LFP(t₀) =

          = ∫{dG(t-T))/G(t-T) – A/G(t-T)}dt

Here we present the model of labour force participation in Sweden. Figure 1 shows that the LFP is very well predicted since 1975. This model is valid for all developed countries. No macroeconomic model can predict the observed changes in LFP using only one macroeconomic parameter. Since the presented model describes the case of Sweden I also mean the latter laureates of the Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel awarded “for their analysis of markets with search frictions” have failed to model the labour market and predict its evolution at the same level of accuracy and forecast horizon.

Why we need the sophisticated model not describing reality if there exists a simple model predicting as accurately as one can only dream?

                  

Figure 1. Observed and predicted LFP in Sweden: T=0.

Inflation in the UK - no sign of deflation any time soon

There exists a long-term equilibrium link between price inflation, CPI_t, unemployment, u_t, and the rate of change of labour force, l_t=dLF/LFdt, as was demonstrated in this blog for many countries. The UK is one of the world biggest economies with a relatively good statistics started chiefly from 1973.  It is a major challenge to model inflation in the UK using our approach.

We have to separate two periods to fit observations: before and after 1985:

CPI_t = 1.0l_t  + u_t  - 0.046; t>1985

CPI_t = -1.0l_t -1.7 u_t + .025; t<1985              (1)

For both periods, inflation does not lag behind unemployment and l_t. Figure 1 presents the observed and predicted CPI curves, all variables were obtained from the OECD database in 2011. All in all, the predictive power of the model is good and timely fits major peaks and troughs. The change from negative to positive linear coefficient in 1985 needs a special explanation. But such effects were observed in other developed countries as well.  A labour force projection could help to predict the future inflation. Since the inflow of new employees is still positive,  l_t >0, and the rate of unemployment does not foresees any dramatic decline in the long run one can be sure that inflation will be positive in the near future.

Figure 1. The rate of CPI inflation in the UK, predicted and measured.

Unemployment in Italy

We introduced a model of unemployment in Italy in 2008 with data available only for 2006. The rate of unemployment was near its bottom at the level of 6%. The model predicted a long-term growth in the rate unemployment to the level of 11% in 2013. In this post we revisit the model. The agreement between the measured and predicted unemployment estimates in Italy validates our concept which states that there exists a long-term equilibrium link between unemployment, u_t, and the rate of change of labour force, l_t=dLF/LFdt. Italy is a unique economy to validate this link because the time lag of unemployment behind l_t  is eleven (!) years. 

The estimation method is trivial – we seek for the best overall fit between observed and predicted curves by trial-and-error method. All in all, the best-fit equation is as follows:

u_t = -5.0l_t-11  + 0.07        (1)

As mentioned above, the lead of l_t is eleven years. This defines the rate of unemployment many years ahead of the current change in labour force. Figure 1 presents two versions of unemployment as defined by the U.S. Bureau of Labor Statistics (BLS) and the OECD. We describe the estimates provided by the OECD (labour force estimates also obtained from the OECD) but have to emphasise that the divergence before 1994 makes it difficult to find a unique model for both agencies.

Figure 2 presents the observed unemployment curve and that predicted using the rate of labour force change 11 years ago and equation (1). Since the estimates of labour force in Italy are very noisy we have smoothed the annual predicted curve with MA(5). All in all, the predictive power of the model is excellent and timely fits major peaks and troughs after 1988. The period between 2006 and 2010 was predicted almost exactly. This is the best validation of the model – it has successfully described a major turn in the evolution of unemployment near its bottom. No other macroeconomic model is capable to describe such dramatic turns many years ahead. As four years ago, we expect the peak in the rate of unemployment in 2013-2014 at the level of 11%.

The evolution of the rate of unemployment in Italy is completely defined 10 year ahead.  Since the linear coefficient in (1) is positive one needs to reduce the growth in labour force in order to reduce unemployment in the 2020s.

 

Figure 1. The rate of unemployment in Italy as measured by the BLS and OECD.

Figure 2. Observed and predicted rate of unemployment in Italy.

The reason of high unemployment in Spain

Here we model the rate of unemployment, u_t, in Spain using its dependence on the change in labor force, l_t=dLF/LFdt. This is another country joining the set of most developed economies with the same relationships between employment and labor force. For Spain, we used data provided by the OECD. Figure 1 depicts unemployment and the change rate of labor force between 1960 and 2010. In line with the OECD description of the breaks in the labor force series: 

Series breaks: In 2005, changes in the questionnaire and the implementation of CATI system in the field work affected the estimates. The 2005 questionnaire produced an additional increase of employment (132 000) and a decrease of unemployment (78 000). From 2001, the new unemployment definition established by the European Commission in 2000 has been introduced. From 1994, persons employed in the “Guardia Civil” are not included in the armed forces. As an indication, this category represented 59 600 people in 1994. In 1976, the lower age limit for inclusion in the Labour Force Survey was raised from 14 to 16, at the same time other modifications to the survey were introduced.

 there are two spikes in the dLF/LF series near 1976 and 2001 as related to step revisions to the level. The spike around 1988 has no explanation in terms of the revisions to labor force, but is of the same amplitude. One can not exclude the opportunity that this spike is related to the processes of joining the EU in 1986.              

As expected, the same functional form of dependence is valid for Spain. The estimation method is based on trial-and-error approach and seeks for the fit between annual curves.  The final model is as follows

u_t = -7.0l_t  + 0.31; t>1986

Figure 2 depicts observed and predicted curves. Before 1986, the curves diverge and another model is likely holds.   Because of high-amplitude oscillations in the original time series for the rate of labour force change, l_t,  we have to smooth it by MA(5). For the period after 1986, R²=0.82. Thus, the change in labor force has been driving the rate of unemployment in Spain. The negative coefficient implies that unemployment is Spain goes down when labor force starts to increase.

 Figure 1. Unemployment rate, u, and the rate of labor force change, l,  in Spain according to the definition introduced by the OECD.

Figure 2. Prediction of inflation by labor force. R²=0.82 for the period between 1986 and 2009.

Low inflation in Germany

There exists a long-term equilibrium link between price inflation, CPI_t, and the rate of change of labour force, l_t=dLF/LFdt, as was shown in this blog for many countries. Germany is a crucial economy to validate this link.  It had a major change in the latest history associated with the reunification. What was the effect of the merge? Here, we model the change in inflation dependence on labour force in 1989. Quantitatively, inflation became less sensitive to the change in labour force by a factor of 4: sensitivity has fallen from -2.2 to - 0.6.  

The estimation method is enhanced relative to our previous studies – the best overall fit is sought by the least squares method as applied to the cumulative curves. In addition to the formal LSQ minimization of the model error we have introduced a varying break year in the model. We allow such a break within 3 years around 1990. By definition, the break year has to provide the lowermost RMS residual. All in all, the best- fit equations for the period before and after 1990 are as follows:

CPI_t = -2.2l_t-6  + 0.046; t<1990

CPI_t = -0.6l_t-6 + 0.018; t>1990           (1)

For both periods, the lead of l_t is six years. This defines the rate of inflation six years ahead of the current change in labour force. Figure 1 presents the observed and predicted CPI curves, all variables were obtained from the OECD database in 2011. All in all, the predictive power of the model is good and timely fits major peaks and troughs. Because the big lag between the change in labour force and inflation one can foresee the change in prices many years ahead. In Germany, one should not expect high price inflation since the level of labour force has not been growing fast.

The coefficient in (1) obtained for the period after 1990 is not well constrained because the change in inflation is small and statistical estimates are not reliable. The future evolution of the overall CPI in Germany will help to resolve the model better. The previous model published in this blog, was obtained for the whole period and did not include the reunification. Corresponding coefficients were -1.71 and 0.041, which are close to those for the period before 1990.

Figure 1. The rate of CPI inflation in Germany, predicted and measured. The lower panel shows the cumulative curves.